%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO068^4.010 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 03:22:40 PM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 158
% Syntax : Number of formulae : 164 ( 40 unt; 0 typ; 20 def)
% Number of atoms : 543 ( 20 equ; 3 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 808 ( 93 ~; 88 |; 1 &; 377 @)
% ( 68 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 106 ( 102 usr; 93 con; 0-2 aty)
% Number of variables : 164 ( 34 ^; 128 !; 2 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p7,type,
p7: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_p6,type,
p6: $i > $o ).
thf(ty_p1,type,
p1: $i > $o ).
thf(ty_p5,type,
p5: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_p4,type,
p4: $i > $o ).
thf(ty_p0,type,
p0: $i > $o ).
thf(ty_p2,type,
p2: $i > $o ).
thf(ty_p10,type,
p10: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_p9,type,
p9: $i > $o ).
thf(ty_p8,type,
p8: $i > $o ).
thf(ty_p3,type,
p3: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( p10 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p1 @ X1 ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP15
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( p0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) )
=> sP22 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP32
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP23
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP26
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( p10 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP33
=> ( sP30
=> sP41 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP30
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP26
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP15
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP22
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] : ( p10 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP46
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP33
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP30
=> sP41 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP33
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP23
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( sP33
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( p0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP33
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP3
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( irel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] : ( p0 @ X1 ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] : ( p0 @ X1 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ sP63,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP51
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP20
| ~ sP33
| sP63 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP16
| ~ sP22
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP44
| ~ sP46
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP17
| ~ sP41
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP56
| ~ sP30
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP11
| ~ sP24
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP48
| ~ sP26
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| ~ sP3
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP10
| ~ sP32
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP19
| ~ sP15
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP37
| ~ sP23
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP6
| ~ sP33
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP31
| ~ sP33
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP2
| ~ sP33
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP45
| ~ sP33
| sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP29
| ~ sP33
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP8
| ~ sP33
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP62
| ~ sP33
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP54
| ~ sP33
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP67
| ~ sP33
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP60
| ~ sP33
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP28
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP58
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP14
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP35
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP55
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP66
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP21
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP7
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP27
| sP67 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP4
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP50
| ~ sP22
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP52
| ~ sP46
| sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP25
| ~ sP41
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP47
| ~ sP30
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP1
| ~ sP24
| sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP38
| ~ sP26
| sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP68
| ~ sP3
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP36
| ~ sP32
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP49
| ~ sP15
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP64
| ~ sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP23
| ~ sP64 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(45,plain,
( ~ sP61
| ~ sP23
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP53
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP65
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP18
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP34
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP5
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP57
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP42
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP9
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP43
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP59
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP40
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(axiom11,axiom,
sP40 ).
thf(axiom10,axiom,
sP59 ).
thf(axiom9,axiom,
sP43 ).
thf(axiom8,axiom,
sP9 ).
thf(axiom7,axiom,
sP42 ).
thf(axiom6,axiom,
sP57 ).
thf(axiom5,axiom,
sP5 ).
thf(axiom4,axiom,
sP34 ).
thf(axiom3,axiom,
sP18 ).
thf(axiom2,axiom,
sP65 ).
thf(axiom1,axiom,
sP51 ).
thf(refl_axiom,axiom,
sP53 ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,h2,axiom11,axiom10,axiom9,axiom8,axiom7,axiom6,axiom5,axiom4,axiom3,axiom2,axiom1,refl_axiom]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,57,h2]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[58,h0]) ).
thf(0,theorem,
! [X1: $i] : ( p0 @ X1 ),
inference(contra,[status(thm),contra(discharge,[h1])],[58,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO068^4.010 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Oct 9 01:34:08 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % Mode: cade22grackle2xfee4
% 0.20/0.44 % Steps: 208
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------